Simple glossy balls in Blender internal renderer
I think you should simply find a better balance between the "mirror" and the "specular" function of the material, as picture 1.



If you really want to fake the reflections, you could render the previous scene, then render only balls, lights and white reflective plane over a transparent background, unchecking the "traceable" option of the material (this will delete the cross reflection between balls, but shadows also will disappear); then composite the two images: floor and shadows from the first render, balls with no cross-reflections from the second (you will miss the shadows of balls over others balls).
This method works also for animation movies.